Tk_MaintainGeometry and Tk_UnmaintainGeometry make it easier for geometry managers to deal with slaves whose masters are not their parents.
Three problems arise if the master for a slave is not its parent:

If the master window,
or any of its ancestors up to the slave's parent,
is moved,
then the slave must be repositioned within its parent in order to maintain the correct position relative to the master.

If the master or one of its ancestors is mapped or unmapped,
then the slave must be mapped or unmapped to correspond.

None of these problems is an issue if the parent and master are the same.
For example,
if the master or one of its ancestors is unmapped,
the slave is automatically removed by the screen by X.

Tk_MaintainGeometry deals with these problems for slaves whose masters aren't their parents.
Tk_MaintainGeometry is typically called by a window manager once it has decided where a slave should be positioned relative to its master.
Tk_MaintainGeometry translates the coordinates to the coordinate system of slave's parent and then moves and resizes the slave appropriately.
Furthermore,
it remembers the desired position and creates event handlers to monitor the master and all of its ancestors up to (but not including) the slave's parent.
If any of these windows is moved,
mapped,
or unmapped,
the slave will be adjusted so that it is mapped only when the master is mapped and its geometry relative to the master remains as specified by x,
y,
width,
and height.

When a window manager relinquishes control over a window,
or if it decides that it does not want the window to appear on the screen under any conditions,
it calls Tk_UnmaintainGeometry.
Tk_UnmaintainGeometry unmaps the window and cancels any previous calls to Tk_MaintainGeometry for the master-slave pair,
so that the slave's geometry and mapped state are no longer maintained automatically.
Tk_UnmaintainGeometry need not be called by a geometry manager if the slave,
the master,
or any of the master's ancestors is destroyed: Tk will call it automatically.

If Tk_MaintainGeometry is called repeatedly for the same master-slave pair,
the information from the most recent call supersedes any older information.
If Tk_UnmaintainGeometry is called for a master-slave pair that is isn't currently managed,
the call has no effect.